The mechanical behavior of collagenous tissues crucially depends on the fibers’ micro-geometry. Herein, we systematically analyze this ubiquitous class of tissues. Finite element simulations of periodic cells enable us to relate the macroscopic tissue response to the mechanical processes of the underlying microstructure. We examine cells with a single thick fiber and cells with a bundle of seven thin fibers while keeping the fraction of the fiber substance identical in both cells. Models with shallow and wrinkled fibers are examined in both cases. Plane stress conditions are imposed, where the stretching direction is aligned with or inclined to the fiber direction. The latter mimics the loading state in the arterial wall. To even better mimic the physiological state, we superimpose a 10% prestretch in the transverse direction. Overall, the stress-stretch curves are bilinear with a low initial slope that converges into a steeper slope as the fibers straighten. This recruitment process becomes even more pronounced under aligned loading. Our expectation that the thick fiber model will be stiffer than the seven fibers bundle model due to its larger bending stiffness turned out to be inaccurate. Analysis of the stresses in the surrounding matrix material revealed that this counterintuitive occurrence is due to a through-matrix interaction between the fibers in the bundle.